x^2-1000x+2=0

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Solution for x^2-1000x+2=0 equation: 


Simplifying
x2 + -1000x + 2 = 0

Reorder the terms:
2 + -1000x + x2 = 0

Solving
2 + -1000x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1000x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -1000x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1000x + x2 = 0 + -2
-1000x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1000x + x2 = -2

The x term is -1000x.  Take half its coefficient (-500).
Square it (250000) and add it to both sides.

Add '250000' to each side of the equation.
-1000x + 250000 + x2 = -2 + 250000

Reorder the terms:
250000 + -1000x + x2 = -2 + 250000

Combine like terms: -2 + 250000 = 249998
250000 + -1000x + x2 = 249998

Factor a perfect square on the left side:
(x + -500)(x + -500) = 249998

Calculate the square root of the right side: 499.997999996

Break this problem into two subproblems by setting 
(x + -500) equal to 499.997999996 and -499.997999996.


Subproblem 1
x + -500 = 499.997999996

Simplifying
x + -500 = 499.997999996

Reorder the terms:
-500 + x = 499.997999996

Solving
-500 + x = 499.997999996

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '500' to each side of the equation.
-500 + 500 + x = 499.997999996 + 500

Combine like terms: -500 + 500 = 0
0 + x = 499.997999996 + 500
x = 499.997999996 + 500

Combine like terms: 499.997999996 + 500 = 999.997999996
x = 999.997999996

Simplifying
x = 999.997999996


Subproblem 2
x + -500 = -499.997999996

Simplifying
x + -500 = -499.997999996

Reorder the terms:
-500 + x = -499.997999996

Solving
-500 + x = -499.997999996

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '500' to each side of the equation.
-500 + 500 + x = -499.997999996 + 500

Combine like terms: -500 + 500 = 0
0 + x = -499.997999996 + 500
x = -499.997999996 + 500

Combine like terms: -499.997999996 + 500 = 0.002000004
x = 0.002000004

Simplifying
x = 0.002000004


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {999.997999996, 0.002000004}

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